Wide bandwidth digital predistortion system with reduced sampling rate

ABSTRACT

A digital predistortion linearization method is provided for increasing the instantaneous or operational bandwidth for RF power amplifiers employed in wideband communication systems. Embodiments of the present invention provide a method of increasing DPD linearization bandwidth using a feedback filter integrated into existing digital platforms for multi-channel wideband wireless transmitters. An embodiment of the present invention utilizes a DPD feedback signal in conjunction with a low power band-pass filter in the DPD feedback path.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/552,231, filed on Nov. 24, 2014; which is a continuation of U.S.patent application Ser. No. 13/777,194, filed on Feb. 26, 2013, now U.S.Pat. No. 8,913,689; which is related to U.S. patent application Ser. No.13/625,760, filed on Sep. 24, 2012, now U.S. Pat. No. 8,873,674, thedisclosures of which are hereby incorporated by reference in theirentirety for all purposes. U.S. Pat. No. 8,149,950, issued on Apr. 3,2012 is hereby incorporated by reference in its entirety for allpurposes.

BACKGROUND OF THE INVENTION

The present invention generally relates to wideband communicationsystems using multiplexing modulation techniques. More specifically, thepresent invention relates to a method of increasing instantaneous oroperational bandwidth for digital predistortion linearization in orderto compensate for nonlinearities and/or memory effects in multi-channelwideband wireless transmitters.

The linearity and efficiency of radio frequency (RF) power amplifiers(PAs) have become critical design issues for non-constant envelopedigital modulation schemes with high peak-to-average power ratio (PAR)values. This has happened as a result of the increased importance ofspectral efficiency in wireless communication systems. RF PAs havenonlinearities which generate amplitude modulation—amplitude modulation(AM-AM) distortion and amplitude modulation—phase modulation (AM-PM)distortion at the output of the PA. These undesired effects may createspectral regrowth in the adjacent channels, as well as in-banddistortion which may degrade the error vector magnitude (EVM).Commercial wireless communication systems may for example employ abandwidth in the range of 20 MHz to 25 MHz. In such an example, thesespectral regrowth effects create an undesired impact over a frequencyband which is more than 100 MHz to 125 MHz wide. The potential impactsmay include inter-system and intra-system interference. Therefore, thereis a need in the art for improved methods and systems related tocommunications systems.

SUMMARY OF THE INVENTION

It is advisable to employ a linearization technique in RF PAapplications in order to eliminate or reduce spectral regrowth andin-band distortion effects. Various RF PA linearization techniques havebeen proposed in the literature such as feedback, feedforward andpredistortion. One of the most promising linearization techniques isbaseband digital predistortion (DPD), which takes advantage of recentadvances in digital signal processors. DPD can achieve better linearityand higher power efficiency with a reduced system complexity whencompared to the widely-used conventional feedforward linearizationtechnique. Moreover, a software implementation provides the digitalpredistorter with a re-configurability feature which is desirable formulti-standards environments. In addition, a PA using an efficiencyenhancement technique such as a Doherty power amplifier (DPA) is able toachieve higher efficiencies than traditional PA designs, at the expenseof linearity. Therefore, combining DPD with a DPA using an efficiencyenhancement technique has the potential for maximizing system linearityand overall efficiency.

Requirements for instantaneous bandwidth (for example, exceeding 25 MHz)for next generation wireless systems continue to increase, which meansthat the DPD processing speed needs to be increased accordingly. Thishigher processing speed may result in new digital platform designefforts, which can often take several months and significant staffresources and costs to complete. The higher processing speed can alsoresult in higher system costs and increased power consumption due tosampling rate increases for DPD in Field Programmable Gate Arrays(FPGAs), digital-to-analog converters (DACs), and analog-to-digitalconverters (ADCs). In addition, RF/IF filter requirements are morestringent, which will also likely increase system costs and complexity.Another typical result of having DPD with a wider instantaneousbandwidth may be increased memory effects. This may cause the DPDalgorithm to become much more complex and will take longer to design,optimize and test.

Embodiments of the present invention provide DPD linearization methodsand systems that provide wider bandwidth without adding a high degree ofcomplexity and cost.

Accordingly, embodiments of the present invention overcome thelimitations previously discussed. Embodiments of the present inventionprovide a method of increasing DPD linearization bandwidth withoutcostly modifications to an existing digital platform for multi-channelwideband wireless transmitters. To achieve the above objects, accordingto some embodiments of the present invention, a DPD feedback signal isemployed along with a narrow band-pass filter in the DPD feedback path.The embodiments described herein are able to extend the DPD bandwidthobtainable with an existing digital transmitter system, without changesin digital signal processing components, which could result in increasedpower consumption and/or cost.

Numerous benefits are achieved by way of the present invention overconventional techniques. As described more fully herein, the digitalfinite impulse response (FIR) filter characteristic for DPD output isimportant in order to avoid the overlapping of distortions, which cancause errors in an indirect learning algorithm based on DPD output andfeedback input. This can result in the need to utilize digital FIRfilters with a large number of taps. Embodiments of the presentinvention may provide for the removal of the digital FIR filter by usinga direct learning algorithm based on DPD input and feedback input.Accordingly, embodiments of the present invention may decrease thenumber of multipliers for multiband applications and even for singleband applications. Moreover, an analog filter characteristic in theanalog feedback path may also be provided in order to avoid theoverlapping of distortions, which can cause errors in the calculation ofcoefficients. Thus, embodiments of the present invention reduce oreliminate the need for one or more multi-pole ceramic filters, which arebig and expensive, replacing them with one or more less-stringentceramic filters that only removes aliasing in the feedback ADC.Accordingly, the digital FIR filter with a large number of taps can beinserted in order to avoid the overlapping. Furthermore, one filter canbe shared for multiband applications. Consequently, embodiments of thepresent invention can utilize a normal ceramic filter and one sharpdigital filter with a large number of taps. These and other embodimentsof the invention along with many of its advantages and features aredescribed in more detail in conjunction with the text below and attachedfigures.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects and advantages of the invention can be more fullyunderstood from the following detailed description taken in conjunctionwith the accompanying drawings in which:

FIG. 1 is a simplified flowchart illustrating a method of increasing DPDlinearization bandwidth according to an embodiment of the presentinvention.

FIG. 2 is a schematic block diagram illustrating a multi-carrierwideband power amplifier system according to an embodiment of thepresent invention.

FIG. 3 is a schematic block diagram illustrating a multi-carrierwideband power amplifier system according to another embodiment of thepresent invention.

FIGS. 4A-4D are graphs showing the DPD bandwidth characteristics for aconventional system.

FIGS. 5A-5D are graphs showing the DPD bandwidth characteristicsaccording to an embodiment of the present invention.

FIG. 6 is a plot showing spectral output response for a conventionalsystem employing DPD and

FIGS. 7A-7C are plots showing spectral output response for systemsaccording to various embodiments of the present invention.

FIG. 8 shows a block diagram of the elements of a Digital Predistorter

FIG. 9 shows a block diagram of Digital Predistortion CoefficientEstimator with a bandwidth-constrained filter

FIGS. 10A-10B are plots showing spectral output response for systemsusing a Digital Predistortion with a bandwidth-constrained filter in thecoefficient estimator.

DETAILED DESCRIPTION OF THE INVENTION

In general, the DPD techniques of the present invention can effectivelyimprove the adjacent channel power ratio (ACPR). However, DPDperformance suffers from the limited bandwidth associated with the speedlimitation of the ADC employed in the DPD feedback path. This ADC iscritical to processing the DPD feedback signals. Although modifying aproduct design to employ an ADC with a higher sampling rate would likelylead to enhanced DPD performance, that approach would increase thecomplexity and cost of the DPD function and would therefore result inhigher system cost. This is obviously an undesirable approach formeeting new and evolving system requirements. In order to overcome theselimitations, the present invention utilizes the bandpass characteristicof the duplexer associated with frequency division duplex wirelesssystems, so that the DPD is only required to provide distortionreduction over the reduced bandwidth of the PA output signals. Thesystem provided by the present invention is therefore referred to as anenhanced-bandwidth digital predistortion (EBWDPD) system hereafter.Embodiments of the EBWDPD system are illustrated with respect to theaccompanying drawings.

In conventional systems, the bandwidth associated with the DPD system istypically required to be five times the bandwidth of the input signal.For example, for a conventional system with a 20 MHz input signalbandwidth, the DPD function requires at least 100 MHz bandwidth for theDPD output and DPD feedback input, which means that feedback ADCsampling rate should be at least 200 Msps. This is a critical factor fora conventional DPD implementation.

FIG. 2 is a schematic block diagram illustrating a multi-carrierwideband power amplifier system according to an embodiment of thepresent invention. The system illustrated in FIG. 2 comprises digitalcomplex input samples 201 (with bandwidth of 20 MHz), digitalpredistortion circuits 202 (with bandwidth exceeding 100 MHz), a digitalfilter 203 with a similar bandwidth to that of the feedback band-passfilter 204 (FB BPF), digital-to-analog converters 205, an IQ modulatorshown as AQM 206, a power amplifier 207, a duplexer 208 (with bandwidthof 20 MHz), radio frequency down-conversion circuits 209 with a lowpower feedback RF band-pass filter 204 (RF FB BPF) for the outputcoupled at the output of the PA 210, and an analog-to-digital converter210 (with a bandwidth typically greater than the RF FB BPF bandwidthobtained by employing a sampling rate greater than two times the FB BPFbandwidth value) for the DPD feedback path. The RF FB BPF 204 filtersthe feedback signal to provide a signal characterized by a reducedbandwidth in comparison with the output of the power amplifier. DPDcoefficients are extracted from the feedback signal produced by the RFFB BPF 204, which has a reduced bandwidth associated with the filter204.

The DPD 202 introduces distortion components associated with the 3rdorder and 5th order expansion of the input signal, which causes the DPDoutput bandwidth to be larger than approximately 100 MHz based on a 20MHz input signal. In order to avoid instability of the DPD algorithm dueto inaccurate error calculation from the DPD output (with bandwidthexceeding 100 MHz) and feedback signal (with FB BPF bandwidth), the DPDoutput is filtered by a digital filter 203 having a bandwidth valuesimilar to that of the RF FB BPF 204. Embodiments of the presentinvention utilize an RF FB BPF 204 with a suitable bandwidth value asdescribed more fully in relation to FIGS. 7A-7C. The bandwidth of filter204 is less than the DPD bandwidth, which contrasts with conventionalsystems in which filter 204 would have a bandwidth equal to the DPDbandwidth. Additionally, the ADC 210 has a bandwidth associated with theFIR filter 203 in some embodiments, which is less than the DPDbandwidth.

It should be noted that in comparison with conventional systems, thebandwidth of various components in the multi-carrier wideband poweramplifier system illustrated in FIG. 2 are reduced, thereby reducingsystem complexity and cost. As an example, the digital filter 203 has abandwidth similar to that of the feedback band-pass filter 204 ratherthan exceeding 100 MHz based on the bandwidth of the digitalpredistortion circuits. The ADC 210 has a bandwidth typically greaterthan the RF FB BPF bandwidth obtained by employing a sampling rategreater than two times the FB BPF bandwidth value. Thus, embodiments ofthe present invention utilize components that operate at lowerbandwidths and sampling rates than conventional components in aconventional system, reducing the system cost and complexity.

FIG. 3 is a schematic block diagram illustrating a multi-carrierwideband power amplifier system according to another embodiment of thepresent invention. This embodiment shares some common features with thesystem illustrated in FIG. 2 as well as some differences. As illustratedin FIG. 3, the system includes a low power narrowband IF band-passfilter 301. Embodiments of the present invention provided by the systemillustrated in FIG. 3 may be easier and less costly to design andimplement using an IF BPF filter compared to using an RF band-passfilter. With an IF filter, the present invention is applicable tosystems employed with various applications based on the use of a commonIF frequency. As was the case for the embodiment shown in FIG. 2, thefeedback ADC following the IF FB BPF employs a sampling rate greaterthan two times the FB BPF bandwidth value for the DPD feedback path.This helps reduce the implementation cost while providing highperformance. The feedback loop provides inputs (e.g., a measure ofdistortion in the power amplifier 207) that are used to introducedistortion that compensates for the amplifier distortion.

The embodiments shown in FIGS. 2 and 3 may employ a digital filter 203characterized by a bandwidth that is less than the bandwidth (e.g., >100MHz) used in conventional systems. Additionally, the embodiments shownin FIGS. 2 and 3 may include either a low power feedback IF BPF or an RFBPF coupled to the PA output. Thus, filtering can be performed at RF orIF according to various embodiments of the present invention.

FIGS. 4A-4D are graphs showing the DPD bandwidth characteristics for aconventional system. The DPD bandwidth for conventional systems isrequired to be greater than 5 times the value of the input signalbandwidth. FIG. 4A shows the DPD input signal. FIG. 4B shows thefeedback signal, with distortion components (dark shading) over a fairlywide bandwidth of FB BW. FIG. 4C shows the DPD output signal withpredistortion components (based on the feedback signal) along with theFIR digital filter bandpass characteristic. The signal withpredistortion components has a bandwidth of slightly less than the DPDbandwidth. FIG. 4D shows the PA/duplexer output signal with distortionhaving been canceled. The data is included in the central spectral bandand distortion is illustrated in FIG. 4B and a distortion component witha 180 degrees phase shift (out of phase) is illustrated in FIG. 4C,resulting in cancellation of the distortion and the signal illustratedin FIG. 4D, with no significant out of band power. In some embodiments,the signal at the output of DPD 202 is similar to that illustrated inFIG. 4B.

As illustrated in FIG. 4D, the duplexer bandwidth is slightly greaterthan the bandwidth of the data spectrum. Embodiments of the presentinvention utilize the filtering properties of the duplexer 208 to assistin removing some of the out of band power from the spectrum. Because ofthe use of the duplexer, it is not necessary to correct across theentire bandwidth (e.g., FB BW), but only a portion of the bandwidth withthe duplexer providing a filtering function.

FIGS. 5A-5D are graphs showing the DPD bandwidth characteristicsaccording embodiments of the present invention. As explained above inrelation to FIG. 2, the DPD bandwidth is associated with the FB BPFbandwidth, which is less than the bandwidth required by conventionalsystems. FIG. 5A shows the DPD input signal. FIG. 5B shows the bandwidthof the feedback signal after the FB BPF 204. As illustrated in FIG. 5B,the bandwidth of the feedback signal after the FB BPF 204 is reduced incomparison to the DPD bandwidth. Thus, referring to FIG. 2, RF feedbackband pass filter (RF FB BPF) 204 has a bandwidth as illustrated in FIG.5B. This bandwidth is reduced in comparison to the DPD bandwidth.

FIG. 5C shows the DPD output signal with predistortion components (basedon the feedback signal) along with the narrower FIR digital filterbandpass characteristic, compared to that for a conventional system. Thesignal with predistortion components has a bandwidth of much less thanthe DPD bandwidth. As illustrated in FIG. 5C, the predistortioncomponent 430 (see FIG. 4C) is greater than the predistortion component530. This results from the filtering properties provided by RF FB BPF204. It should be noted that the bandwidth associated with thepredistortion component 530 is much narrower than the DBD BW.

FIG. 5D shows the PA/duplexer output signal. In contrast with FIG. 4D,the Duplexer has a significant role in reducing output distortion welloutside the bandwidth of the input signal. Close to the respective bandedges of the desired signal, the DPD provides a substantial amount ofdistortion reduction. Thus, using the filtering properties of theduplexer enables compensation over a smaller range than otherwiseavailable. Close to the carrier, the out of band power (outside the dataspectrum) is substantially zero as a result of the digital predistortiontechniques used herein. Although some out of band power is present, themajority of the power is outside the bandwidth of the duplexer,resulting in the majority of the power being filtered by the duplexer.

FIG. 6 is a plot showing spectral output response for a conventionalsystem employing DPD. The results in FIG. 6 are for a conventional PAsystem without any FB BPF. The results are for a 4 carrier WCDMA inputsignal (with a total bandwidth of 20 MHz) and 60 W average output power.The bandwidth of the distortion is ˜100 MHz (i.e., 5 times the signalbandwidth). DPD reduces distortion more than 20 dB.

FIGS. 7A-7C are plots showing spectral output response for systemsaccording to various embodiments of the present invention. The spectrumshown in FIGS. 7A-7C illustrate DPD performance based on various valuesof FB BPF bandwidth (FIR filter 203) (25 MHz, 30 MHz and 40 MHzrespectively). With 25 MHz FB BPF bandwidth, the spectrum associatedwith DPD performance includes noise at a predetermined level. Systemsusing FB BPF bandwidths of 30 MHz and 40 MHz provide results for DPDperformance that are comparable to the DPD performance for conventionalsystems, while utilizing an ADC 210 having a much lower sampling ratethan the feedback ADC employed in a conventional system, which maybe >100 MHz. Additionally, embodiments of the present invention utilizea filter 203 that is characterized by much lower bandwidth than aconventional filter in a conventional system which has a typical valueof bandwidth greater than five times the signal bandwidth. The systembandwidth (i.e., 25 MHz) refers to the feedback loop and the bandwidthof RF FB BFP 204 in FIG. 2 or IF FB BPF 301 in FIG. 3.

Table 1 is a table showing Adjacent Channel Leakage Power Ratio (ACLR)performance for embodiments of the present invention, whose values aretaken from results of FIG. 6 and FIGS. 7A-7C. Table 1 is a table thatshows in various rows the ACLR performance of: PA system without DPD, PAwith conventional DPD approach, PA with DPD with 25 MHz FB BPF accordingto the present invention, PA with DPD with 30 MHz FB BPF according tothe present invention and PA with DPD with 40 MHz FB BPF according tothe present invention. Based on the data shown in Table 1, systemsutilizing a FB BPF with 30 MHz minimum bandwidth are able to achieveperformance similar to the conventional PA with DPD. Therefore, someembodiments of the present invention utilize a 30 MHz feedback pathbandwidth, meaning that a feedback ADC with a sampling rate of only 60Msps can be employed. This contrasts with conventional DPD systems thatrequire a feedback ADC with 200 Msps or greater sampling rate forsimilar performance.

In some embodiments, a 60 Msps feedback ADC is used for a 20 MHzinstantaneous input signal bandwidth and a Duplexer is used with 25 MHzbandwidth. In some embodiments, a Duplexer is used that has a bandwidthslightly larger than the instantaneous or operational input signalbandwidth. In some embodiments, the value of feedback bandwidth is setat a value approximately 20% greater than the instantaneous oroperational input signal bandwidth. In some embodiments, a system whichsupports a 60 MHz instantaneous or operational input signal bandwidthhas its value of feedback bandwidth set to 72 MHz, such as would resultfrom employing a feedback ADC with a 144 Msps sampling rate. Thus,embodiments of the present invention provide benefits (including reducedcost and complexity) not available using a conventional DPD systememploying a feedback ADC with a 250 Msps sampling rate, which is apopular choice for many conventional DPD systems.

TABLE 1 ACLR ACLR SYSTEM DESCRIPTION (dBc) @ +5 MHz(+10 MHz) (dBc) @ −5MHz(−10 MHz) PA without DPD −37.1(−38.8) −28.2(−30.37) Conventional DPD/−51.64(−51.83)/−52.29(−53.21) −50.38(−51.14)/−50.84(−52.57) System(25MHz) DPD(25 MHz)/System(25 MHz) −47.89(−45.6)/−48.72(−47.2) −46.8(−45.46)/−47.46(−47.01) DPD(30 MHz)/System(25 MHz) −50.85(−50.2)/−51.54(−51.75)  −50.0(−50.84)/−50.49(−52.23) DPD(40MHz)/System(25 MHz) −51.35(−51.45)/−51.99(−52.88)−50.33(−51.46)/−50.79(−52.85)

As illustrated in Table 1, the power amplifier without DPD has an ACLRvalue of −37.1 dBc and −28.2 dBc at +5 MHZ and −5 MHz, respectively.Using a conventional system, values of −51.64 dBc, etc. and −50.38 dBc,etc. are achieved. Utilizing embodiments of the present invention, asshown on the last three lines, values of −47.89 dBc, −50.85 dBc, and−51.35 dBc, respectively, are achieved. Thus, although performance isslightly degraded for the 25 MHz system of the present invention,performance improves for the 30 MHz system and is substantiallyequivalent for the 40 MHz system. Thus, embodiments of the presentinvention can utilize systems operating over a much narrower bandwidth(i.e., 40 MHz) than conventional DPD systems (i.e., 100 MHZ).

FIG. 1 is a simplified flowchart illustrating a method of increasing DPDlinearization bandwidth according to embodiments of the presentinvention. The method 100 includes receiving a complex input signal at aDPD (101) and introducing predistortion to the signal using the DPD(102). The method also includes filtering the predistorted signal usinga digital filter (103) and converting the filtered signal to an analogsignal (104). Filtering the predistorted signal can be performed over afilter bandwidth less than the bandwidth of the DPD, for example, over afilter bandwidth between 30 MHz and 50 MHz.

The method further includes quadrature modulating the analog signal(105), amplifying the modulated signal (106), coupling a portion of theamplified signal to provide a feedback signal (107), and filtering thefeedback signal using a band-pass filter (108). Filtering the feedbacksignal using the band-pass filter can be performed over a band-passbandwidth less than the bandwidth of the DPD, for example, the band-passbandwidth can be between 30 MHz and 50 MHz.

Additionally, the method includes downconverting the filtered feedbacksignal (109), converting the downconverted signal to a digital signal(110), and providing the digital signal to the DPD at its feedback input(111). Converting the downconverted signal can be performed at asampling rate less than twice the bandwidth of the DPD, for example, ata sampling rate is between 60 Msps and 100 Msps.

FIG. 8 is a schematic diagram showing an embodiment of the DigitalPredistorter system in accordance with the invention. The DPD 803illustrated in FIG. 8 is analogous to DPD 202 in FIG. 2. As illustrated,u(n) is the input signal to the digital predistorter 803. The digitalcomplex baseband input signal samples are multiplied by complexcoefficients drawn from the LUT entries or from a polynomial.x(n)=u(n)·F _(m)(|u(n)|)where F_(m)(|u(n)|) is the complex coefficient corresponding to an inputsignal magnitude for compensating AM to AM and AM to PM distortions ofthe power amplifier. The memoryless LUT or polynomial coefficients canbe estimated by the following equation, which is the least mean square(LMS) algorithm with indirect learning.F _(m)(|u(n+1)|)=F _(m)(|u(n)|)+μ·u(n)·e(n)where n is the iteration number, μ is the stability factor and errore(n)=x(n)−y(n)·F_(m)(|x(n)|). The indirect learning algorithm iscontained in the Coefficient Estimator block. This invention is alsoapplicable to a memory based LUT or polynomial. In addition to thepolynomial or LUT predistorter 802, the DPD 803 also includes acoefficient estimator 801. The output of the DPD is provided at x(n) toan interpolator or DAC, for example to FIR filter 203 and DAC 205 inFIG. 2. The feedback path provides feedback signal y(n), for example,received from ADC 210 in FIG. 2.

FIG. 9 shows a block diagram of the Coefficient Estimator 904(illustrated by reference number 801 in FIG. 8). The CoefficientEstimator 904 includes a polynomial Function generator 901, a BandwidthConstrained Filter 902, also referred to as a digital filter, and aLeast Square Algorithm 903. The Function generator 901 creates all thenonlinear components used in the digital predistorter. The BandwidthConstrained Filter (i.e., the digital filter) 902 restricts thebandwidth of the nonlinearities. In an embodiment, the bandwidth of thenonlinearities is restricted to ensure that they match those of theanalog feedback filter in the system. The Least Square algorithm 903optimizes the complex coefficients in order to reduce or minimize theerror in the indirect learning algorithm.

FIGS. 10A and 10B demonstrate the performance of the bandwidthconstrained filter. FIG. 10A shows the performance when a 30 MHzbandwidth constrained filter is used. FIG. 10B shows the performancewhen a 50 MHz bandwidth constrained filter is used. The performanceclose to the carriers is comparable to the conventional full bandwidthDPD, however outside the constrained filter bandwidth the performancedegrades to the PA output without DPD. The Duplexer that is used afterthe power amplifier will eliminate the nonlinearities that remainoutside the bandwidth of the constrained filter.

Although the present invention has been described with reference to thepreferred embodiments, it will be understood that the invention is notlimited to the details described thereof. Various substitutions andmodifications have been suggested in the foregoing description, andothers will occur to those of ordinary skill in the art. Therefore, allsuch substitutions and modifications are intended to be embraced withinthe scope of the invention as defined in the appended claims.

What is claimed is:
 1. A wideband communications system comprising: adigital predistorter (DPD) operable to receive an input signal, whereinthe DPD is characterized by a first bandwidth; a filter characterized bya second bandwidth coupled to the output of the DPD; a digital-to-analogconverter coupled to the output of the filter; a modulator coupled tothe output of the digital-to-analog converter; a power amplifier coupledto the output of the modulator; a band-pass filter characterized by athird bandwidth coupled to the output of the power amplifier; adown-converter coupled to the output of the band-pass filter; and ananalog-to-digital converter (ADC) coupled to the output of thedown-converter, wherein the ADC is characterized by a sampling ratevalue less than a value of the first bandwidth, wherein the DPDcomprises a coefficient estimator applying an indirect learningalgorithm.
 2. The wideband communications system of claim 1, wherein thesampling rate value of the ADC is less than one-third the value of thefirst bandwidth.
 3. The wideband communications system of claim 1,wherein the third bandwidth is less than the first bandwidth.
 4. Thewideband communications system of claim 1, wherein the third bandwidthis substantially equal to the second bandwidth.
 5. The widebandcommunications system of claim 1, wherein the band-pass filter comprisesa low power narrowband band-pass filter.
 6. The wideband communicationssystem of claim 1, wherein the filter comprises a narrowband digitalfilter.
 7. The wideband communications system of claim 1, wherein theband-pass filter comprises a radio frequency (RF) filter.
 8. Thewideband communications system of claim 1, wherein the coefficientestimator comprises a polynomial function generator, a digital filter,and a least square algorithm.
 9. The wideband communications system ofclaim 1, further comprising a duplexer coupled to the output of thepower amplifier.
 10. A method of operating a communications system, themethod comprising: receiving a signal at a digital predistorter (DPD);introducing predistortion to the signal using the DPD; filtering thepredistorted signal using a digital filter; converting the filteredsignal to an analog signal; modulating the analog signal; amplifying themodulated signal; coupling a portion of the amplified signal to providea feedback signal; filtering the feedback signal using a band-passfilter; downconverting the filtered feedback signal; converting thedownconverted signal to a digital signal; and providing the digitalsignal to a coefficient estimator in the DPD, wherein the coefficientestimator applies an indirect learning algorithm.
 11. The method ofclaim 10, wherein filtering the predistorted signal is performed over afilter bandwidth less than a bandwidth of the DPD.
 12. The method ofclaim 10, wherein filtering the feedback signal using the band-passfilter is performed over a band-pass bandwidth less than a bandwidth ofthe DPD.
 13. The method of claim 10, wherein converting thedownconverted signal is performed at a sampling rate less than twice thebandwidth of the DPD.
 14. The method of claim 10, wherein providing thedigital signal to the coefficient estimator in the DPD comprises:creating nonlinear components of the digital signal; restricting abandwidth of the nonlinear components; and optimizing coefficients inthe DPD.